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Chapter 2: Problem 51

Raindrops fall to the ground from a cloud \(1700 \mathrm{~m}\) above Earth's surface. If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground? Would it be safe to walk outside during a rainstorm?

Short Answer

Expert verified
The raindrops would be moving at a speed of approximately 183 m/s when they strike the ground. It would not be safe to walk outside during a rainstorm if raindrops were falling at these speeds.

Step by step solution

01

Identify Knowns and Unknowns

In this situation, three quantities are known: the initial speed \(u = 0 \; \mathrm{m/s}\) (because the raindrops start from rest), the acceleration \(g = 9.8 \; \mathrm{m/s^2}\) (average acceleration due to Earth's gravity), and the dislocation \(s = 1700 \; \mathrm{m}\). The aim is to find the unknown variable, the final speed \(v\).
02

Choosing the Relevant Equation

The equation \(v^2 = u^2 + 2gs\), which derives from the equations of motion, will be used to calculate the final speed \(v\). This equation connects the final speed with the initial speed, the acceleration due to gravity and the distance covered, all of which are known quantities.
03

Substituting Known Values into the Equation

Substitute all known values into the chosen equation: \(v^2 = 0 + 2 * 9.8 * 1700\). Therefore, \(v^2 = 33320\).
04

Solve for the Unknown Variable

Isolate the variable \(v\) by taking the square root of both sides: \(v = \sqrt{33320}\). Therefore, \(v \approx 183 \; \mathrm{m/s}\). This is the final speed of the raindrops when they strike the ground.
05

Analyze the Safety of Walking outside during a Rainstorm

The calculated speed is very high, a raindrop moving at approximately 183 m/s is moving at a speed faster than most commercial jet planes. Therefore, walking outside in such a rainstorm would be extremely dangerous.

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Most popular questions from this chapter

At a construction site a pipe wrench strikes the ground with a speed of \(24.0 \mathrm{~m} / \mathrm{s}\). (a) From what height was it inadvertently dropped? (b) For how long was it falling?

On a dry road a car with good tires may be able to brake with a deceleration of \(11.0 \mathrm{mi} / \mathrm{h} / \mathrm{s}\left(=4.92 \mathrm{~m} / \mathrm{s}^{2}\right) .(a)\) How long does it take such a car, initially traveling at \(55 \mathrm{mi} / \mathrm{h}(=24.6\) \(\mathrm{m} / \mathrm{s}\) ), to come to rest? \((b)\) How far does it travel in this time?

A car is driven east for a distance of \(54 \mathrm{~km}\), then north for \(32 \mathrm{~km}\), and then in a direction \(28^{\circ}\) east of north for \(27 \mathrm{~km}\). Draw the vector diagram and determine the total displacement of the car from its starting point.

A ship sets out to sail to a point \(124 \mathrm{~km}\) due north. An unexpected storm blows the ship to a point \(72.6 \mathrm{~km}\) to the north and \(31.4 \mathrm{~km}\) to the east of its starting point. How far, and in what direction, must it now sail to reach its original destination?

A woman walks \(250 \mathrm{~m}\) in the direction \(35^{\circ}\) east of north, then \(170 \mathrm{~m}\) directly east. (a) Using graphical methods, find her final displacement from the starting point. (b) Compare the magnitude of her displacement with the distance she walked.
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